This project encompasses a number of topics in physics and applied mathematics related to chemical reaction rates, the qualitative behavior of dynamical systems, blood flow in capillaries and the development of theory related to problems in optical imaging in turbid media. The use of lasers for diagnostic purposes are based on such a theoretical underpinning. We have provided a theoretical explanation of phenomena observed in measurements of plaque buildup in human tissues. A study of the chemical reaction A+B->C in a one dimensional geometry has been expanded by deriving more detailed solutions to the underlying diffusion-reaction equations. By carrying out this generalization we have demonstrated the theoretical possibility of having a reaction front that moves non-monotonically as a function of time. Concurrent experiments by Professor R. Kopelman at the University of Michigan have verified that this indeed occurs in real chemical systems. A third project dealt with the extension of present models for indicator-dilution models which specifically model rate processes as being of first order. These are widely used in the interpretation of physiological experiments on the exchange of molecules between tissue and blood vessels. Current theories are based on very specific models which have not been checked experimentally. We have shown how to derive a non-Markovian version of the theory, which permits the description of qualitatively different behavior than that following from the standard models. These also form a more general framework for interpreting experimental data.